Lemma 5 (Sharir and Agarwal [1]}, page 191) 
The combinatorial complexity \(K(F)\)  of the lower envelope of a collection \(F\)  of \(n\)  (partially defined) bivariate functions that satisfy the assumptions below is \(O(n^{2+\varepsilon })\) , for any \(\varepsilon >0\) .The theorem, as stated in the book (Theorem 7.7), includes some additional assumptions, but the book then shows that they are not essential.
